Constructions of symplectic LCD MDS codes from quasi-cyclic codes
Xia Huang, Jin Li, Shan Huang · Advances in Mathematics of Communications · 2022
Linear complementary dual (LCD) codes play an important role in data storage, communications systems and cryptography. In this paper, we construct some symplectic LCD codes from quasi-cyclic (QC) codes, and prove that these symplectic LCD codes with dimension two over \begin{document}$ \mathbb{F}_{2^a} $\end{document} are maximum-distance-separable (MDS) codes. By extending the generator matrices of symplectic LCD MDS codes with dimension two, we obtain a series of symplectic LCD codes over \begin{document}$ \mathbb{F}_{2^a} $\end{document} . As an application, some new entanglement-assisted quantum error-correcting codes (EAQECCs) over \begin{document}$ \mathbb{F}_{2^a} $\end{document} are constructed by symplectic LCD codes.